Graph Of Linear Equation In Two Variable

This is a well-known fact that a linear equation has infinitely many solutions.
And the solutions are written as pairs of values.

For example, the solution of the linear equation in two variables x + 2y = 6 can
be expressed in the form of a table as given below:

x

2

0

6

4

...

y

2

3

0

1

...

On a graph paper these points (2, 2), (0, 3), (6, 0) and (4, 1) are plotted. Now
if any two points are joined, a straight line AB is obtained. Hence the geometrical
representation of equation x + 2y = 6 is a straight line.

All the points which lie on the line AB satisfy the equation x + 2y = 6. For example,
if we take points (6, 0), (2, 2) then,

Now plotting the points (-1, 3) and (4, 1) on the graph paper and joining these
with the help of a ruler we get the line which is the graph of the equation 2x +
5y = 13.
In the above representation, we can clearly see that the point (2, 5) does not lie
on the graph and hence x = 2, y = 5 is not a solution of the given equation.

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